How do you solve 5- \frac { a - 11} { a + 4} = \frac { a ^ { 2} - 1} { a + 4}?

Dec 28, 2016

$a = 8$

Explanation:

$5 - \frac{a - 11}{a + 4} = \frac{{a}^{2} - 1}{a + 4}$

$5 = \frac{{a}^{2} - 1}{a + 4} + \frac{a - 11}{a + 4}$

$5 = \frac{\left({a}^{2} - 1\right) + \left(a - 11\right)}{a + 4}$

$5 \left(a + 4\right) = {a}^{2} - 1 + a - 11$

$5 a + 20 = {a}^{2} + a - 12$

$0 = {a}^{2} + a - 12 - 5 a - 20$

$0 = {a}^{2} - 4 a - 32$

$0 = \left(a - 8\right) \left(a + 4\right)$

$a - 8 = 0 , a + 4 = 0$

$a = 8 , a = - 4$

$a \ne - 4$, because it would result in dividing by $0$

$a = 8$